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Membrane-bound Turing patterns
Physical Review E, 2005Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other
Herbert, Levine, Wouter-Jan, Rappel
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Complex Systems, 2023
The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
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The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
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Physical Review E, 1999
We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
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We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
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Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
Journal of Mathematics and PhysicsReaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding network dynamics theories have been continuously enriched with the advancement of network science.
Junyuan Shi, Linhe Zhu
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1998
In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
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In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
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Localized Turing and Turing-Hopf Patterns
1995In systems driven away from thermodynamic equilibrium, patchiness often arises through the occurrence of symmetry breaking bifurcations. Diffusive instabilities resulting from differential diffusion processes acting in the presence of some autocatalytic kinetic scheme enter that class of phenomena to produce stationary space periodic (Turing) or ...
Borckmans, Pierre +5 more
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Turing patterns with cellular computers
Cell SystemsTuring patterns are a key theoretical foundation for understanding organ development and organization. While they have been found to occur in natural systems, implementing new biological systems that form Turing patterns has remained challenging. To address this, Tica et al.1 used synthetic genetic networks to engineer living cellular computers that ...
Grozinger, Lewis, Goñi-Moreno, Ángel
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Turing Instability and Pattern Formation in a Strongly Coupled Diffusive Predator-Prey System
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2020We are concerned with the Turing instability and pattern caused by cross-diffusion in a strongly coupled spatial predator–prey system. We explore how cross-diffusion destabilizes the spatially uniform steady state which is stable in reaction–diffusion ...
Guangping Hu, Zhaosheng Feng
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Sidewall forcing of hexagonal Turing patterns: rhombic patterns
Physica D: Nonlinear Phenomena, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pérez-Muñuzuri, V. +4 more
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Turing-Type Patterns on Electrode Surfaces
Science, 2001We report stationary, nonequilibrium potential and adsorbate patterns with an intrinsic wavelength that were observed in an electrochemical system with a specific type of current/electrode-potential ( I- φ DL ) characteristic.
Li, Y. +5 more
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